inside the life satisfaction blackbox

LEONARDO BECCHETTI, LUISA CORRADO AND PAOLA SAMÀ

Chapter 1

INSIDE THE LIFE SATISFACTION BLACKBOX

2Leonardo Becchetti, Department of Economics, Law and Institutions (DEDI), University of Rome Tor Vergata (Italy). E-mail: [email protected]

Luisa Corrado, Department of Economics, Law and Institutions (DEDI), University of Rome Tor Vergata (Italy) and University of Cambridge (UK). E-mail: [email protected]; [email protected]

Paola Samá, Department of Economics, Law and Institutions (DEDI), University of Rome Tor Vergata (Italy). E-mail: [email protected]

W O R L D H A P P I N E S S R E P O R T 2 0 1 6 | S P E C I A L R O M E E D I T I O N

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Executive summary

We propose an alternative measure of life satisfaction to the standard, synthetic cognitive well-being question, based on the specific contribution of 11 life-satisfaction sub-compo-nents (including satisfaction about the past, life opportunities, hope for the future, vitality, control over one’s life, meaning of life). The alternative measure is either estimated as a latent factor, obtained as a simple unweighted average from the above mentioned sub-compo-nents, or extracted with principal component analysis. We document that the new dependent variable fits much better standard socio-demo-graphic controls and corrects the “Danish life satisfaction bias” in the direction suggested by the vignette approach. These findings do not reject our theoretical assumption that the alter-native measures derived from the life satisfac-tion sub-components are less noisy and less culturally biased and therefore perform better than the standard self-reported life satisfaction. The straightforward policy advice of the paper is to introduce the above-mentioned sub-compo-nents (similarly to what happens with sub-ques-tions used to calculate the General Health Questionnaire score) in an additional question to measure more effectively subjective well-being.

Introduction

Investigation into the determinants of life satisfaction has boomed in recent years due to the availability of worldwide information on subjective well-being at the individual level in many well-known surveys (such as the German Socioeconomic Panel, the British Household Panel Survey, and the Gallup World Poll). The topic is of particular importance for at least four reasons. First, it provides an alternative independent source (beyond experimental evidence) for testing previously undemonstrat-ed assumptions about the human preferences (or social norms) affecting subjective well-be-ing, which are at the basis of all theoretical economic models. Second, it provides valuable evidence of a widening range of factors affect-ing life satisfaction, beyond the dimension of observed choices. This helps us to understand the importance of, among other factors, relative comparisons, hedonic adaptation, experienced utility, and the relationship between expecta-tions and realizations.1 Third, it sheds lights on as-yet-unexplored and important aspects of economic reality (i.e. the measurement of the shadow value of non-market goods2) with relevant policy insights. Fourth, it provides information and evidence for the debate on reforming well-being indicators: If straightfor-wardly maximising happiness is not a good idea for various reasons, happiness studies may provide stimulating insights on what the well-being indicators that have been currently adopted may have left behind.

In spite of the great potential of the findings of life-satisfaction literature, many methodological problems challenge its validity. These problems are related to the interpersonal and inter-country comparability of the standard measure, self-de-clared subjective well-being, which lacks of cardinality. The vignette approach is a recent attempt to overcome the problem.3 The approach corrects for individual heterogeneity by using differences across individuals to evaluate a common situation (the vignette), with the same

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response categories as the self-assessment question. However, as is well known, even this approach has limits, since the two hypotheses on which it hinges (vignette equivalence and response consistency4) are often rejected by empirical tests.5

Our paper’s contribution is to define a theoreti-cal framework which aims to improve upon standard subjective well-being measures, and predicts that three alternative measures of life satisfaction will be superior in terms of their capacity to reduce the dependent variable noise and cultural biases captured by country dum-mies. The approach is based on the measuring of 11 life-satisfaction sub-components.

Our main argument is that, when asked to formulate their life-satisfaction score, individu-als intuitively weight different sub-components (evaluation of past life, opportunities for the future, overall meaning of their own life, vitality, etc.). Since the operation is not easy, the general, abstract life-satisfaction question incorporates much more noise and measurement error than a latent variable, which may be extracted by using direct answers to each of the abovemen-tioned, implicit sub-components.

A second argument supporting our main as-sumption is that the sub-component questions are much more straightforward and easy to answer when they are formulated on a 1–4 range (as in the SHARE database we use in this pa-per), in which any number is associated with an adjective whose meaning can be grasped imme-diately. On the contrary, in the standard 0–10 life-satisfaction questions, there is no verbal correspondence for each of the scale’s numerical values. Finally, we postulate that the sub-compo-nent approach also offers an additional advan-tage: Country-specific cultural biases (also due to the different nuances of the translation of the term “life satisfaction” in different languages) tend to be much larger on the general questions than when averaging sub-components, or

extracting from them the error-free, latent life-satisfaction factor.

We test our hypothesis on data from the SHARE database where, to the standard life-satisfaction question, “How satisfied are you with your life, all things considered?” with responses on a scale from 0 (completely dissatisfied) to 10 (complete-ly satisfied),we add an additional question on the life-satisfaction sub-component. The question relates to 11 items:

1. How often do you think your age prevents you from doing the things you would like to do?

2. How often do you feel that what happens to you is out of your control?

3. How often do you feel left out of things?

4. How often do you feel that you can do the things that you want to do?

5. How often do you feel that family responsi-bilities prevent you from doing what you want to do?

6. How often do you feel that a shortage of money stops you from doing the things that you want to do?

7. How often do you look forward to another day?

8. How often do you feel that your life has meaning?

9. How often, on balance, do you look back to your life with a sense of happiness?

10. How often do you feel full of energy these days?

11. How often do you feel that life is full of opportunities?


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For each item, answers are given on a 1–4 scale with an adjective (often, sometimes, rarely, never) being matched to any value.6

Our findings document that the three alternative approaches (estimated latent life-satisfaction regressing the standard 0–10 answer on the 11 life-satisfaction sub-components, unweighted average of the 11 life-satisfaction sub-compo-nents, extraction of the first principal compo-nent from principal component analysis on the sub-components) greatly improve the goodness-of-fit of our baseline life-satisfaction estimate, with respect to the use of the standard life-satis-faction question. The adjusted R-squared grows by around 15 points (20 points when sub-compo-nents interact with socio-demographic controls and country dummies to calculate predicted life satisfaction), and the AIC and BIC scores con-firm the improvement.

These findings support our theoretical hypothe-sis that the three alternative measures reduce the dependent variable noise. We further docu-ment that our three approaches correct the well-known Danish cultural bias in life satisfac-tion answers,7 which we find in our data as well.8 Our approaches therefore provide, in this re-spect, results similar to the vignette approach, without requiring the two limiting assumptions of vignette equivalence and response consistency.

The straightforward policy advice stemming from our paper is that to obtain a better measure of subjective well-being, surveys should intro-duce additional questions, including the above mentioned sub-components. Since one addition-al question with the 11 sub-points is enough to achieve the goal, our results indicate that the trade-off between improving the quality of data and enriching surveys with more precise ques-tions on different well-being dimensions bears clearly in favor of such a decision. We also note that what we propose for life satisfaction is akin to the approach used to construct another well-being index (the General Health Question-

naire9 score in the BHPS), used to measure emotional prosperity; it is the average of 12 mental distress sub-questions.

The paper is divided into five sections (including Introduction and Conclusions), organized as follows. In the second section, we illustrate our theoretical framework and the two hypotheses to be tested. In the third section, we discuss de-scriptive findings and present our econometric specifications. In the fourth section, we present and discuss econometric findings and illustrate several robustness checks. The fifth section presents our conclusion.

Theoretical Framework

We conceive of the “true” cognitive measure of subjective well-being for the i–th individual as a latent variable which is a weighted average of j different components (vitality, evaluation over past life, outlook at the future, money and leisure satisfaction, being in control over one’s own life, meaning of life, etc.):

E(LS*i) =

iZ*

i (1)

where E(LS*i) is the expected value of true overall

life satisfaction for the i–th individual, while Z*

i ={Z

ij} is a j ∑ 1 column vector in which sub-

components have – weights – i = {

ij} is a j ∑ 1

vector of parameters - measuring their specific impact on the synthetic life satisfaction evaluation.10

Our assumption is that, when individuals are directly asked the standard life satisfaction question (LS), the random component is larger due to the higher difficulty of i) understanding the more general question (in itself and compar-atively across countries due to the different language nuances); ii) matching a different, more intuitive verbal evaluation to any numerical value of the response scale, and iii) averaging its different components without explicitly mentioning them.11 We therefore consider our

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dependent variable,12 the standard life-satisfac-tion question, as characterised by measurement error within the classical errors-in-variables framework, and by a fully observed, continuous dependent variable.13 Hence, when the standard question is formulated, surveys capture the following variable:

LSi = LS*

i + v

i (2)

where vi represents the measurement error and

E(vi) ≠ 0. More specifically, we assume that v

i

has a country specific (c) and an individual

specific (i) bias.

vi =

c +

i (3)

Conversely, when individual i-th is asked about the j-th components we obtain:

Zij = Z*

i + v~

ij (4)

where

v~ij = ~

cj + ~

ij

is also a measurement error which captures individual bias ~

ij (i.e. due to a misunderstand-

ing of the specific Z question or to a difficulty of the individuals in evaluating correctly his/her situation) and country-specific bias ~

cj (i.e. due to

cultural and linguistic differences in the way the life satisfaction sub-component question is understood in different countries or to strategic answering that is a social/cultural tendency to overestimate or underestimate own levels of life satisfaction for each sub-component).

We assume, however, that the bias disappears when using individual components as far as the number of components increases and the number of interviewed individuals grows so that EZ

i EZ*

i where Z

i = {Z

ij}. As stressed by Bound

et al.,14 in the presence of exogenous determi-

nants of the error ridden variables,15 or, in some cases, multiple indicators of the same outcome, it is possible to use them as instruments to infer the “true” value of life satisfaction. Hence, using Z

i as the set of instruments for LS*

i we assume

that E(LS*i | Z*

i) is a strict linear function of Z

*i so

that these multiple indicators are orthogonal to the error implying Cov(Z*

i , v~

i)=0 and there is no

measurement error, hence E (v~i)=0.

The measurement error term of the synthetic question LS

i does not go to zero as far as the

number of interviewed individuals grows, implying E(v

i) ≠ 0 for at least three reasons.

First, the life satisfaction term is more abstract than a straightforward question on its compo-nents (vitality, evaluation of part life, etc.). Second, it requires a quick calculus of (1) and of the weights of the individual Z

i components

which is not easy and intuitive. It is for instance highly likely that cultural differences affect the more abstract life satisfaction question, while they cancel out when using the more straightfor-ward set of Zi

questions. Finally, the sub-compo-nent questions are much more straightforward and easy to answer when they are formulated on a 1–4 range since in this instance any number is associated to an adjective whose meaning can be grasped immediately. On the contrary, in the 1–10 scale life-satisfaction question there is no verbal correspondence for each of the scale values. This is why the conditional expectation of the error term, v

i, may be significantly different from

zero when we adopt the synthetic question on life satisfaction. Hence, a more articulated set of questions on the set of Z

i components may

produce a much richer and accurate measure of cognitive subjective well-being.

To understand the implications of measurement errors when we adopt a synthetic answer on life satisfaction, suppose that we estimate the following relationship for life satisfaction:

LS*i =

0 + ' d

i + ' X

i +

i (5)


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i = 1,…, N c = 1,…, C – 1 (6)

where 0 denotes a constant, d

i =

{d

ic} is a

(C– 1) ∑ 1 vector of country dummies, with d

ic = 1 if individual i is resident in country c and

is the corresponding (C– 1) ∑ 1 vector of coefficients. X

i = {X

ik} with k=1, …, K denotes a

(K–1) ∑ 1 vector of controls and is the corre-sponding K ∑ 1 vector of coefficients. Finally,

i

is an individual error term which is normally distributed with E(

i) = 0.

If the synthetic answer for life satisfaction is observed with error we get:

LSi =

0 + ' d

i + ' X

i + e

i (7)

Notice that the error term is now ei =

i +

v

i. This

means that if we estimate the model, we would see the error in measurement appearing in the new error term. If the measurement error is correlated with the independent variables, this also implies a violation of the assumption that the conditional expectation of the error should be zero.

By the OLS assumptions, i should be uncorrelat-

ed with the covariates and consequently should not present any problem.16 Looking at the measurement error, v

i, if it is independent from

the regressors Cov(Xi , v

i)=0 and E(v

i) ≠ 0, the

estimate of the coefficients will still be unbiased but measured with less precision. However, if both E(v

i) ≠ 0 and Cov(X

i , v

i) ≠ 0, the endogene-

ity between vi and X

i induced by the measure-

ment error implies that the estimates of the coefficients may also be biased.

The other main problem comes from inference since var (

i + v

i ) = 2

+ 2

v > 2

. The last

inequality means that the estimated variance is larger than when using the true life satisfaction measure, which means that inference is liable to type I error. Collecting more data in the form of multiple components for the dependent

variable could be a solution also to this problem, since more observations imply a better estima-tor of variance, and consequently reduce errors in inferences.

In this instance, the SHARE questions allow us to measure some fundamental components of the life-satisfaction evaluation such as: vitality, a negative evaluation of the past life, a positive look at the future, absence of monetary con-straints, sensation that life is meaningless, feeling in control of one’s own life, sense of not being left out, perception of having time beyond family duties, and freedom of choice. As it is clear from these attributes, the components of life satisfaction in the survey include an outlook on the past and on the future, money and leisure satisfaction, vitality and control over one’s own life, plus an eudaemonic definition of life satis-faction (meaning of life). This is why they can be considered a good deal richer than the simple, standard cognitive synthetic question. An additional advantage of the question on sub-components is that a unique and different verbal modality is attached to each numerical value of the ordinal scale. This makes the an-swer easier and more intuitive and may help to counteract the measurement error, v

i.

What we propose is the use of the estimated latent life satisfaction:

LS*i =

0 + ' Z

i +

i (8)

where is a j ∑ 1 vector of coefficients. Here, the use of multiple components allows the counter-action of the measurement error in the sub-com-ponents as defined in (4) implying E(

i)=0. We

use the predicted value of life satisfaction:

L̂S*i

= ̂0 + ̂' Z

i (9)

as the dependent variable of our benchmark estimate in (5) which is a more correct measure of LS*

i than the observed synthetic question

8

LSi

= LS*i + v

i under the assumption that the

weights in (7) are correctly estimated i.e. ̂ij

= ij

i, j.

Alternatively, our second approach consists of simply averaging the sub-components to obtain:

which is equal to the previous measure under the assumption that

ij = 1. The limit of this

second approach is that it is contradicted by empirical evidence in case the –weights are different from one. The advantage is that it has less noise if, for some reasons (i.e. endogeneity), we think that the estimated weights do not coincide with actual weights ( ̂

ij ≠

ij ).

A third approach which may overcome the problem of overlaps and correlations among the different components of life satisfaction is the principal component approach. On the basis of the approach, we will extract the first orthogonal factor accounting for the higher share of the variance and use such a variable as dependent variable in our estimate (see section 3).

Hypothesis Testing

Given our assumptions, a first testable hypothe-sis is that the goodness-of-fit of the model using the latent variable LS*

i is better than that of the

model using the declared life satisfaction LSi. In

fact, in the presence of measurement error in a model for declared life satisfaction, LS

i, the

variance of residual grows, implying that both the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) will be higher, while the adjusted R2 will be lower, indicating a poorer performance.17

A second testable hypothesis related to country dummies is that our approach should be effec-tive in reducing country bias (measured by the significance of country dummies in vignette responses) in the expected direction.

Descriptive Finding and Benchmark Model Specification

We use data from the second wave of SHARE (which covers only European citizens over 50) including interviews run between 2006 and 2007,18 which is the only wave including the crucial information on the 11 happiness sub-com-ponents. Table 1 provides the list of variables and Figure 1 reports the histogram of self-reported life satisfaction, while Table 2 illustrates some descriptive findings of our sample.

Self-reported life satisfaction has the usual right-skewed distribution, with a mean of 7.54 and about 60 percent of respondents declaring a self-reported life satisfaction above 6 (Figure 1). All answers to the 11 life satisfaction sub-ques-tions have averages between 2.5 and 3.5 (the range is 1–4) with the lowest average for the sub-components related to age-preventing activities, and lack of money (items 1 and 5 of the 11 sub-questions, see introduction) (Table 2). The sample is almost perfectly balanced in terms of gender characteristics (females are 49.9 percent), while the average years of educa-tion are 10.5. Half of the sample is between 50 and 60 years old. Average household size is 2.25 (Table 2).

Our baseline estimate of life satisfaction is

LSi =

0 + ' d

i + ' X

i + e

i (10)

As is well known, the dependent variable (self-reported life satisfaction) is ordinal, so its estimation would require something like an ordered logit or probit. However, as Ferrer–i–Carbonell and Frijters19 (2004) argue, cardinal


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estimation seems to perform just as well as ordinal estimation in this context.20

Regressors used are those standard in this literature and include a gender dummy (taking value one if the respondent is male), years of education, household size, the number of children, and the number of grandchildren. Marital status is measured by five dummies (married, divorced, separated, widowed, living with regular partner) with single status as the reference category. Age is controlled for with six age class dummies with age 50–55 as the refer-ence category. Four dummies (big city, large town, small town, and suburbs, with rural as the reference category) capture characteristics of the place of residence.

The SHARE database gives us the opportunity to control for a large number of health factors, such as various physical disabilities and a number of reported illnesses. We measure them synthetically with three variables, which sum many specific single items in the three domains (see Table 1 for details). We finally add a set of variables measuring voluntary work, religious attendance, participation in sports and social activity, helping in families, and leaving an inheritance.

As is well known, the SHARE database has a very large number of individuals who refuse to report income, and many missing values for other important variables. We therefore follow an approach that is standard in previous empiri-cal studies on this dataset by using Christelis’ data on imputed gross total household income included in the Share database,21 and calculated following the Fully Conditional Specification methods (FCS) of Van Buuren et al.22 The imputations23 are country-specific in the sense that they are made separately for each country,24 and the sample is representative of the popula-tion aged 50 and above. The main scope of this procedure is to generate the distribution of the missing value of a specific variable, conditional

on the value of the observed values of other non-missing variables in the dataset. The SHARE database provides data obtained with this procedure by creating five imputed datasets. We therefore end up having five different values (one for each iteration) of the imputed variables. In what follows, we propose estimates using just one of them, while performing robustness checks using the other four iterated values. Variables with imputed variables in our specifi-cation are the log of household income, and a number of other variables characterised by item non-response: number of children; number of grandchildren; number of rooms in the main residence; and whether the respondent lives in a big city, suburbs/outskirts of a big city, large town, small town, or rural area or village.25

Econometric Findings

In the benchmark estimate where the dependent variable is the 0–10 standard life-satisfaction question, the adjusted R-squared is .217 and the AIC and BIC criteria are equal to 112,824.6 and 112,924.4 respectively (Table 3, column 1). The model includes many controls, but the Variance Inflation Factor (VIF) shows that there are no significant problems of multicollinearity.26 The log of imputed household income and education years are positive and significant as expected. Consistent with the empirical literature, we find that being married and living with a partner significantly increase life satisfaction compared to being single. The household size has a nega-tive sign, presumably a proxy for the impact of household size on the individual portion of gross total household income. Living in big cities impacts positively, while the age-dummy effects grow with age.27 The number of grand-children positively affects self-declared life satisfaction, while the number of children does not. All three variables indicating health prob-lems are negative and significant, while those measuring social life (participation in sports, helping members of the family, doing volunteer work) are mostly positive and significant. Inheri-

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tance transmission during life is also positively associated to our dependent variable. Most country dummies are significant and are expect-ed to include two components: country-specific omitted variables affecting life satisfaction (such as climate, institutions, and cultural effects) and heterogeneity in life satisfaction scales (country bias). We will try to identify country bias in what follows by testing whether country dummies are significant when the dependent variable is the respondents’ evaluation of the same vignette.

To produce estimates from the first alternative approach, we estimate the latent life satisfaction factor with the following specification

LS*i =

0 + ' Z

i +

i (11)

in which the standard life satisfaction variable is regressed on the 11 life satisfaction sub-compo-nents (the Z-variables) described in the introduc-tion and = {

j} with j = 1,…, 11 denotes the

corresponding 11 ∑ 1 vector of coefficients. Note that the correlation matrix of the different happiness components displays a maximum correlation between the future good and oppor-tunities variables (around .63). Other strong correlations are between vitality and, respective-ly, future good (around .54) and opportunities (56 percent) (Table 4).

All the regressors are strongly significant as expected and the adjusted R-squared is around 39 percent (Table 5, column 1). The VIF shows that there are no multicollinearity problems in this estimate. The most important component is future perspectives (future good), but the evalua-tion of the past (past good) is also strongly significant, confirming that life satisfaction is the product of a weighted average of different sub-components including an evaluation of the present, the past, and the perspective on one’s future life (future perspectives). For an idea of the magnitude of these effects, when the model is re-estimated as an ordered logit, a unit in-crease in future perspectives adds 3.3 percent to

the likelihood of declaring the highest level of life satisfaction, while positive evaluation of the past only adds 2.4 percent (Table 5, column 3).

The predicted value of the regression in (2):

L̂S*i

= ̂0 + ̂'Z

i (12)

is then used as dependent variable in the base-line model in (1) which becomes

L̂S*i

= 0 + 'd

i + 'X

i + ~e

i (13)

The baseline model with the modified depen-dent variable has a much better goodness-of-fit (from .217 to .342). The AIC and BIC (76,647.54 and 76,747.01) are also considerably improved (Table 3, column 2).

When comparing the sign and significance of the regressors between standard and alternative models we find that: i) life satisfaction is not increasing with age anymore; ii) the magnitude of income and the significant marital status variables (married and with regular partner) is reduced, even though the regressors remain significant; iii) house size becomes significant; iv) the significance of geographical dummies changes. Magnitudes and signs of all the other variables remain remarkably stable.

The first alternative method has several limits. First, it still uses in the first stage the dependent variable whose limit we want to overcome. Second, the estimated coefficients in the regres-sion used to calculate the predicted latent life satisfaction variable may be biased by omitted variables, endogeneity or multicollinearity (even though we documented that the last problem is not severe).

We therefore test the robustness of our theoreti-cal hypotheses with two other alternatives. The first is a simple unweighted average of the life-satisfaction sub-components. We are aware


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that, in this way, we overcome the limit of the latent life satisfaction estimate even though, by using an unweighted average, we assume quite restrictively that the different sub-components have unit weights.

The estimate of the baseline model with the sub-components unweighted average dependent variable provides a goodness-of-fit which is very close to that of our benchmark alternative approach in terms of R-squared (34.2 percent), while improving further in terms of AIC and BIC (35,813.61 and 35,813.49 respectively) (Table 3, column 3).

The other alternative which avoids the arbitrary choice of equal weights is the extraction of a principal component from the life-satisfaction sub-components. The approach has the addition-al advantage of correcting for correlation and potential multicollinearity among different life-satisfaction sub-components (i.e. the answer to the meaning of one’s own life may be correlat-ed with feeling in control, not feeling left out, having a good perspective on the future, etc.). The principal component analysis documents that the first extracted component accounts for 37 percent of the variability of the selected variable. The first component has its strongest correlation with the sub-questions about future perspectives (.38), life opportunities (.37) and vitality (.36) (Tables 6 and 7). The Kaiser-Mey-er-Olin measure of sampling adequacy (.76)28 rejects the hypothesis that the selected variables have too little in common to implement a factor analysis.

When using the first principal component as dependent variable (our third alternative meth-od), we find that the goodness-of-fit is around .35 (Table 3, column 4) with significance and signs of regressors very close to those of the two previous approaches.

The comparison of the goodness-of-fit among the standard model and our three alternatives, in terms of AIC and BIC values, tells us that the best model is the one in which the dependent variable is the unweighted average of sub-com-ponents followed by the one in which we use the predicted life satisfaction estimated on the 11 sub-components. The ranking of the models in terms of adjusted R-squared is, however, differ-ent—since all three models are very close, and outperform by far the standard one, with the unweighted average doing slightly worse. The reason for the different ranking is that the unweighted average model has, by far, the smallest residual sum of squares (which is the crucial factor for AIC and BIC), but also a much smaller total sum of squares (which is the factor on which progress in goodness-of-fit is scaled for when using adjusted R-squared).

Finally, we aim to check whether our approach can correct for country bias. We tackle this issue in the most conservative and simple way. We first average the values of the two life-satisfac-tion vignettes included in the SHARE,29 and then regress the variable on the country dum-mies with/without socio-demographic controls. France is the omitted reference country. The Danish dummy is the highest in magnitude and significance (around .627, t-stat 14.08), followed by the Czech dummy (.474, t-stat 10.50) and the German dummy (.332, t-stat 8.42), indicating that respondents from these three countries overevaluate the common vignette situations in terms of life satisfaction vis à vis the French, who are the reference category. The Danish dummy result is consistent with what is found in the vignette literature as noted in the introduc-tion.30 This gives us confidence in the fact that a cultural bias exists, at least for this country.

We therefore check whether our three approach-es correct country biases in the expected direc-tion. The inspection of the country dummies in the first column of Table 3 (standard life-satisfac-tion estimate) compared with those in the other three columns of the same Table 3 (our three

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alternative approaches) documents that all of the three approaches correct the Danish effect in the desired direction. The Danish dummy is, in fact, .798 in the standard life-satisfaction estimate. It falls to .321 under our first alternative method (life satisfaction predicted on the 11 sub-compo-nents), to .135 when using the second alternative method (unweighted average of sub-compo-nents), and to .454 when using the third alterna-tive method (principal component analysis). Confidence intervals of the Danish dummy from the three alternative methods do not overlap with those of the standard life satisfaction estimate. Note as well that both the Czech and German dummies are corrected in the expected direction (reduction of the positive magnitude) in five out of six cases by the three alternative approaches.

Robustness Check and Discussion

We perform several robustness checks to control whether our main findings are robust to pertur-bations of the benchmark model. First of all we want to control their sensitivity to the imputa-tion variables. We therefore report, for simplici-ty, only goodness-of-fit statistics (and not full regression estimates), considering imputed variable values from the other four iterations. The results are very close to those of the first iteration, consistent with what is found in the literature using the same data (Table 8).

Since the number of observations in the second model is slightly lower than that in the first model, due to some missing values on the life-satisfaction sub-component questions which do not match with missing values on baseline regressors (21,680 against 22,494), we repeat the first estimate with exactly the same valid observations of the second. We find that our con-clusions remain unchanged (Table 9).

In a third robustness check of our first approach, we re-estimate the latent life-satisfaction factor by assuming that the impact of the 11 sub-com-

ponents is not the same according to different countries or crucial sociodemographic factors. More specifically, we interact the sub-compo-nents with all country dummies, age classes, and gender according to the following specifica-tion.

(14)

where dic (c = 1,…, C) denote the country dum-

mies, dia (a = 1,…, A) denote the age dummies

and dig denotes the gender dummy. The good-

ness-of-fit of the estimate jumps to .40 (highest among all models) even though the AIC is almost unchanged with respect to Table 3, column 2 where we use predicted life satisfac-tion from (2) (Table 11). This indicates that there is a clear trade-off with the capacity of correcting country dummies in the right direction. The result is consistent with the fact that overparam-etrization improves goodness-of-fit (as it gener-ally does) at the cost of creating noise on the coefficient values, since the values of the predict-ed life-satisfaction component used as depen-dent variable are affected by many insignificant interacted variables (while the 11 sub-compo-nents in the simple model in Table 5 are all significant).

In another robustness check, we re-estimate the benchmark model from Table 3, excluding the health variables which may be suspected of endogeneity. Last, we eliminate from our specifi-cation all the variables imputed with the Christe-lis et al. (2011) approach,31 to check whether our findings are sensitive to such imputation. Our main findings are robust to these changes (Tables 12 and 13).

Consider, finally, that a peculiarity of our work is that we are comparing models in terms of alternative dependent variables and not, as usually occurs, nested or non-nested models on the basis of differences in the considered set of regressors. An observationally equivalent interpretation of our findings could therefore be


13

that the selected regressors are spurious and that the “true” set of life-satisfaction determi-nants could, in principle, yield a superior goodness-of-fit when using the standard life-sat-isfaction dependent variable. In such a case, the superior goodness-of-fit of the alternative model does not demonstrate, per se, that our alterna-tive dependent variables capture better factors affecting life satisfaction.

What might be argued against this interpreta-tion is that we use regressors (marital status, income, gender, education, etc.) which are standard in the life-satisfaction literature. Fur-thermore, their sign and magnitude does not vary much between the standard and the alterna-tive models. Hence, it is much more reasonable to assume that the considered regressors are the true observable determinants of life satisfaction, and that our alternative dependent variable can be measured with less bias and noise than the standard one, as we assume in our theoretical framework. Last but not least, we demonstrate that the superior goodness-of-fit of the alterna-tive models is robust to several changes in the set of regressors. On such basis, it is hard to imagine an alternative set of observable and “true” life-satisfaction determinants that we did not consider which could justify the observation-ally equivalent interpretation of our result which we mention above.

Conclusion

The standard life-satisfaction question used in surveys is likely to suffer from serious problems of abstraction, complexity of calculus, and cultural bias. Abstraction depends on the fact that its 0–10 scale prevents intuitive correspon-dence with verbal modalities. Complexity of calculus originates from the problem that the overall life-satisfaction evaluation is implicitly derived from a weighted sum of sub-compo-nents affecting it (i.e. money satisfaction, sense of life, outlook at the past, perspectives on the future, vitality, etc.). Cultural bias depends on

the fact that different linguistic nuances in the meaning of the term may enhance differences in answers across individuals from different countries which do not depend on true differ-ences in life satisfaction.

The point we raise in our paper is that the richness of direct and simpler information on the life-satisfaction sub-questions (answers on 1–4 scale on each item with correspondence between an adjective and each numerical value) may significantly reduce these three problems, thereby improving goodness-of-fit and reducing the noise component of country dummies. We articulate our alternative strategy under three different approaches (estimation of the latent life satisfaction regressing the standard life satisfaction variable on the above-mentioned sub-components, simple unweighted average of the subcomponents, extraction of the first principal component among the subcomponents with principal component analysis).

Our findings do not reject the above-mentioned hypotheses. The goodness-of-fit is greatly en-hanced under all of the three alternative ap-proaches. The well known Danish cultural bias, which we find also in our data consistently with similar findings in the vignette literature, is corrected in the desired direction by all of our three approaches.

What our results suggest is that the use of a small set of less-abstract and comprehensive life satisfaction sub-questions increases the share of subjective well-being accounted for by observ-able life events. Since this improvement can be obtained by merely adding one demand to standard surveys (hence a reasonable cost more than compensated by the documented benefits), our straightforward political advice is that new life-satisfaction surveys should all contain such sub-questions. The suggestion we make is very close to what is currently done to calculate a (mental) health index (the General Health Questionnaire score), which has been used as an

14

alternative to self-declared life-satisfaction as a proxy for subjective well-being.32 The index is the unweighted average of 12 mental distress ques-tions and therefore closely follows one of our alternative approaches.

An important element which should be taken into account is that our findings are obtained on a database (SHARE) which includes only indi-viduals aged 50 and above. Future research

should verify whether our findings are equally valid when younger age cohorts are included. This will, however, not be possible until the additional question on life-satisfaction sub-com-ponents is added. We also suggest additional reflection on whether the range of questions applied to the 50+ sample are also applicable to the younger cohorts, or whether a different set of questions should be considered.

Table 1: Variable Legend

VARIABLE DESCRIPTION

Female Dummy var. =1 if respondent is female; =0 otherwise.

Log income Log of household total gross income. Its value is equal to the sum over all household members of the individual-level values of: annual net income from employment and self-employment (in the previous year); Annual public old age/early or pre-retirement/disability pension (or sickness benefits); Annual public unemployment benefit or insurance, public survivor pension from partner; Annual war pension, private (occupational) old age/early retirement/disability pension, private(occupational) survivor pension from partner’s job, public old age supplementary pension/public old age/public disability second pension, secondary public survivor pension from spouse or partner, occupational old age pension from a second and third job; Annual public and private long-term insurance payments; Annual life insurance payment, private annuity or private personal pension, private health insurance payment, alimony, payments from charities received; Income from rent. Values of the following household level variables are added: Annual other hhd members’ net income; Annual other hhd members’ net income from other sources; Household bank accounts, government and corporate bonds, stocks/shares; mutual funds (imputed as in Christelis, 2011).

Education years Years the respondent has been in full time education.

Household size Household size.

Age class Respondent’s age class: = 1 if respondent’s age < 55; = 2 if resp.’s age = [55,59]; = 3 if resp.’s age = [60,64]; = 4 if resp.’s age = [64,69]; = 5 if resp.’s age = [69,74]; = 6 if resp.’s age = [74,79]; = 7 if age > 79.

Leaving inheritance Respondent’s answer to the question: including property and other valuables, what are the chances that you or your husband/wife/partner will leave an inheritance totaling 50,000 euro or more? The possible answers range from 0 to 100.

Married Dummy =1 if the respondent lives with spouse.

Registered partnership

Dummy =1 if the respondent lives with a partner.

Widowed Dummy =1 if the spouse is died.

Divorced Dummy =1 if respondent is divorced.

Separated Dummy =1 if the respondent lives separated from spouse.

Single Dummy =1 if the respondent lives as a single.

N.of children Respondent’s number of children (imputed as in Christelis, 2011).

N.of grandchildren Respondent’s number of grandchildren (imputed as in Christelis,2011).

Hrooms Number of rooms in the main residence (imputed as in Christelis, 2011).

Big city Dummy =1 if the respondent lives in a big city (imputed as in Christelis, 2011).

Suburbs Dummy =1 if the respondent lives in suburbs/outskirts of a big city (imputed as in Christelis, 2011).

Large town Dummy var.=1 if the respondent lives in a large town (imputed as in Christelis, 2011).

Small town Dummy =1 if the respondent lives in a small town (imputed as in Christelis, 2011).

Rural area Dummy =1 if the respondent lives in a rural area or village (imputed as in Christelis,2011).


15

Long-term illness Dummy =1 if the respondent declares any long-term health problems, illness, disability or infirmity.

Survey question: some people suffer from chronic or long-term health problems. By long-term we mean it has troubled you over a period of time or is likely to affect you over a period of time.

Do you have any long-term health problems, illness, disability or infirmity?

No limited activities Dummy =1 if the respondent has not been limited because of a health problem in activities people usually do. Survey question: for the past six months at least,to what extent have you been limited because of a health problem in activities people usually do?

Numb illnesses It is the sum of illnesses the respondent is currently being treated for or bothered (A heart attack including myocardial infarction or coronary thrombosis or any other heart problem including conges-tive heart failure; high blood pressure or hypertension; high blood cholesterol; a stroke or cerebral vascular disease diabetes or high blood sugar; chronic lung disease such as chronic bronchitis or emphysema; asthma; arthritis, including osteoarthritis, or rheumatism; osteoporosis; cancer or malignant tumor, including leukaemia or lymphoma, but excluding minor skin cancer; stomach or duodenal ulcer, peptic ulcer; Parkinson disease; cataracts; hip fracture or femoral fracture; Alzheimer disease, dementia, organic brain syndrome, senility or any other serious memory impairment; benign tumor).

Life satisfaction Respondent degree of life satisfaction. Survey question: On a scale from 0 to 10 where 0 means completely dissatisfied and 10 means completely satisfied, how satisfied are you with your life?

Age no prevent Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often do you think your age prevents from doing the things you would like to do? For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

No out control Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often do you feel that what happens to you is out of control? For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

No feel left out Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often do you feel left out of things? For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

Fred. choice Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often do you feel that you can do the things that you want to do? For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

No fam.responsibility Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often do you feel that family responsibilities prevent you from doing what you want to do?. For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

No lack money Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often do you feel that shortage of money stops you from doing the things that you want to do?. For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

Life meaningful Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often do you feel that your life has meaning? For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

Past good Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often on balance, do you look back to your life with a sense of happiness? For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

Vitality Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often do you feel full of energies these days? For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

Opportunities Respondent degree of statements that have used to describe their lives or how they feel. Survey question: How often do you fell that life is full of opportunities? For each item answers are given on a 1-4 scale where an adjective (often, sometimes, rarely, never) is matched to any value.

Voluntary Dummy =1 if respondent has done voluntary or charity work in the last month.

Table 1: Variable Legend (continued)

Religion attendance Dummy =1 if respondent has taken part in activities of a religious organization (church, synagogue, mosque etc.) in the last month.

Political participation Dummy =1 if the respondent has taken part in a political or community-related organization in the last month.

Help to family Dummy =1 if the respondent has provided help to family,friends or neighbors in the last month.

Cared for sick Dummy =1 if the respondent has cared for a sick or disabled adult in the last month.

Attended education Dummy =1 if the respondent has attended an educational or training course in the last month.

Sport social Dummy =1 if the respondent has gone to a sport, social or other kind of club in the last month.

Figure 1. Distribution of Self Reported Life Satisfaction

16

Table 1: Variable Legend (continued)

De

nsi

ty

1.5

0 2 4 6 8 10

1

.5

lifesat


17

Imputation n.1

VARIABLE Mean Max Min S.dev. N.

Life satisfaction 7.54 10.00 0.00 1.78 32412

Female 0.49 1.00 0.00 0.50 33280

Married 0.71 1.00 0.00 0.45 33254

Log income 10.60 15.32 3.00 1.42 32957

Education years 10.50 25.00 0.00 4.28 32712

Household size 2.25 14.00 1.00 1.08 33280

Age class 3.64 7.00 1.00 1.91 33271

Leaving inheritance 0.58 1.00 0.00 0.43 31428

Married 0.71 1.00 0.00 0.45 33254

Widowed 0.15 1.00 0.00 0.35 33254

Divorced 0.07 1.00 0.00 0.25 33254

Separated 0.01 1.00 0.00 0.11 33280

Registered partner 0.01 1.00 0.00 0.12 33254

Sociability 0.10 0.88 0.00 0.13 32517

Voluntary 0.12 1.00 0.00 0.33 32517

Religion attendance 0.11 1.00 0.00 0.31 32517

Political participation 0.04 1.00 0.00 0.20 32517

Help to family 0.17 1.00 0.00 0.38 32517

Cared for sick 0.07 1.00 0.00 0.26 32517

Attended education 0.07 1.00 0.00 0.26 32517

Sport social 0.20 1.00 0.00 0.40 32517

Age no prevent 2.63 4.00 1.00 1.03 32504

No out control 2.84 4.00 1.00 0.96 32339

No feelleftout 3.05 4.00 1.00 0.96 32400

Fred choice 3.23 4.00 1.00 0.89 32458

No fam. Resp. prevent 3.03 4.00 1.00 0.97 32458

No lack money 2.56 4.00 1.00 1.10 32467

Life meaningful 3.55 4.00 1.00 0.72 32265

Past good 3.38 4.00 1.00 0.76 32172

Vitality 3.15 4.00 1.00 0.86 32486

Opportunities 3.09 4.00 1.00 0.87 32290

Future good 3.07 4.00 1.00 0.88 32077

Long-term illness 0.48 1.00 0.00 0.50 33166

Limitedactivities 0.43 1.00 0.00 0.50 33166

Numbillnesses 1.41 13.00 0.00 1.44 33280

Table 2: Descriptive Statistics

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Table 3: The Determinants of Life Satisfaction Under Standard and Alternative Dependent Variables

VARIABLES Self reported latent life satisfaction

Predicted life satisfaction

Life satisfaction average 11 subcomponents

Principal component: 11 subcomponents

Female 0.022 -0.033 -0.016 -0.066

(0.021) (0.027) (0.013) (0.049)

Log income 0.113*** 0.086*** 0.037*** 0.131***

(0.022) (0.013) (0.006) (0.022)

Education years 0.024*** 0.027*** 0.012*** 0.048***

(0.008) (0.006) (0.003) (0.011)

Household size -0.037** -0.025*** -0.016*** -0.034**

(0.014) (0.007) (0.004) (0.013)

Age class 55-59 0.058** 0.079*** 0.033*** 0.100***

(0.022) (0.015) (0.008) (0.028)

Age class 60-64 0.092* 0.118*** 0.048** 0.149**

(0.047) (0.033) (0.017) (0.065)

Age class 65-69 0.150*** 0.118*** 0.053** 0.124*

(0.045) (0.036) (0.018) (0.069)

Age class 70-74 0.191** 0.095* 0.034 0.028

(0.068) (0.050) (0.025) (0.092)

Age class 75-79 0.204*** 0.052 0.010 -0.110

(0.063) (0.048) (0.025) (0.086)

Age class above 79 0.211** -0.058 -0.056* -0.417***

(0.073) (0.057) (0.028) (0.101)

Leaving inheritance 0.317*** 0.262*** 0.119*** 0.431***

(0.045) (0.025) (0.011) (0.042)

Married 0.479*** 0.185*** 0.067*** 0.309***

(0.079) (0.034) (0.016) (0.060)

Widowed 0.079 0.034 0.016 0.049

(0.065) (0.040) (0.019) (0.072)

Divorced -0.010 -0.060 -0.025 -0.048

(0.082) (0.058) (0.026) (0.100)

Separated -0.104 -0.029 -0.017 -0.011

(0.099) (0.071) (0.033) (0.121)

Registered partner 0.533*** 0.201*** 0.078*** 0.354***

(0.080) (0.042) (0.019) (0.071)

N. of children 0.014 -0.011 -0.008** -0.010

(0.009) (0.007) (0.004) (0.013)

N.of grandchildren 0.011** 0.006** 0.003** 0.008*

(0.005) (0.002) (0.001) (0.004)


19

Hrooms 0.020 0.026** 0.009** 0.037**

(0.012) (0.008) (0.004) (0.014)

Big city 0.105** 0.041 0.016 0.080

(0.047) (0.031) (0.016) (0.058)

Suburbs 0.021 0.055** 0.024* 0.100**

(0.066) (0.023) (0.011) (0.041)

Large town 0.121** 0.084** 0.041** 0.147**

(0.055) (0.035) (0.016) (0.063)

Town 0.123* 0.106* 0.053* 0.185**

(0.058) (0.049) (0.024) (0.085)

Long-term illness -0.206*** -0.142*** -0.068*** -0.267***

(0.029) (0.020) (0.010) (0.036)

Limited activities -0.543*** -0.434*** -0.232*** -0.882***

(0.048) (0.036) (0.018) (0.068)

Numb. Illnesses -0.133*** -0.100*** -0.051*** -0.196***

(0.010) (0.009) (0.005) (0.016)

Voluntary 0.103*** 0.103*** 0.057*** 0.212***

(0.029) (0.020) (0.008) (0.032)

Religion attendance 0.157** 0.110*** 0.044** 0.182**

(0.053) (0.034) (0.019) (0.062)

Political participation 0.152*** 0.087** 0.040** 0.173**

(0.044) (0.036) (0.015) (0.062)

Help to family 0.103*** 0.087*** 0.037*** 0.197***

(0.029) (0.016) (0.009) (0.032)

Cared for sick -0.053* -0.039* -0.043*** -0.059

(0.028) (0.020) (0.010) (0.039)

Attended education 0.023 0.027 -0.001 0.057

(0.038) (0.025) (0.013) (0.045)

Sport social 0.115*** 0.122*** 0.061*** 0.251***

(0.030) (0.024) (0.012) (0.043)

Austria 0.490*** 0.291*** 0.116*** 0.388***

(0.033) (0.027) (0.012) (0.047)

Belgium 0.226*** 0.042*** -0.008** -0.040***

(0.011) (0.007) (0.003) (0.013)

Czech Rep. -0.346*** -0.443*** -0.226*** -0.796***

(0.035) (0.033) (0.015) (0.055)

Switzerland 0.846*** 0.419*** 0.173*** 0.678***

(0.028) (0.015) (0.007) (0.024)

Table 3: The Determinants of Life Satisfaction Under Standard and Alternative Dependent Variables (continued)

20

Spain 0.245*** -0.010 -0.024 -0.093

(0.041) (0.032) (0.015) (0.057)

Germany 0.340*** 0.236*** 0.104*** 0.310***

(0.016) (0.007) (0.003) (0.012)

Greece -0.216*** -0.386*** -0.253*** -0.787***

(0.037) (0.027) (0.013) (0.046)

Denmark 0.798*** 0.321*** 0.135*** 0.454***

(0.046) (0.028) (0.013) (0.048)

Italy 0.059 -0.209*** -0.161*** -0.511***

(0.035) (0.030) (0.015) (0.054)

Netherlands 0.553*** 0.582*** 0.251*** 0.876***

(0.012) (0.006) (0.003) (0.010)

Poland -0.316*** -0.078** -0.053*** -0.135**

(0.053) (0.032) (0.015) (0.058)

Sweden 0.590*** 0.064* 0.016 0.049

(0.059) (0.036) (0.016) (0.060)

Constant 5.54*** 6.22*** 2.57*** -1.84***

(0.26) (0.17) (0.07) (0.29)

Observations 30325.000 29414.000 30427.00 29414.000

R-squared 0.217 0.342 0.342 0.353

Log-Likelihood -56400.000 -38312.000 -17895.00 -55924.000

AIC 112824.600 76647.540 35813.610 111871.800

BIC 112924.400 76747.010 35913.490 111971.300

Robust standard errors in parentheses *** p<0.01, ** p<0.05, *p<0.1Reference Categories: Age class: 50-54; Marital Status: Single; Urban area: Rural; Country: France.

Table 3: The Determinants of Life Satisfaction Under Standard and Alternative Dependent Variables (continued)


21

Table 4: Correlation Matrix

Life-sat

Age no

prev

No out control

No fel-

leftout

Fred of choice

No fam resp.

No lack money

Life mean-ingful

Past good

Vitality Oppor-tunity

Future good

Lifesat 1.00

Age no prev 0.33 1.00

No out control 0.33 0.43 1.00

No felleft out 0.38 0.39 0.53 1.00

Fred of choice 0.31 0.25 0.21 0.25 1.00

No fam resp. 0.16 0.14 0.19 0.21 0.07 1.00

No lack money 0.33 0.23 0.21 0.26 0.18 0.28 1.00

Life meaningful 0.42 0.25 0.26 0.32 0.33 0.06 0.17 1.00

Past good 0.37 0.17 0.18 0.24 0.23 0.09 0.20 0.44 1.00

Vitality 0.42 0.40 0.34 0.35 0.36 0.06 0.17 0.44 0.33 1.00

Opportunity 0.45 0.34 0.28 0.32 0.37 0.08 0.25 0.46 0.38 0.56 1.00

Future good 0.50 0.36 0.31 0.35 0.37 0.09 0.29 0.49 0.40 0.54 0.63 1.00

Table 5: The Impact of Subjective Well-Being Sub-Components on Self-Declared Life Satisfaction

OLS Ordered LOGIT Ordered LOGIT (marginal effects)*

VARIABLES Life satisfaction Life satisfaction Life satisfaction

Life satisfaction

Age no prevent 0.080*** 0.134*** 0.009***

(0.012) (0.013) (0.015)

No out control 0.104*** 0.145*** 0.102***

(0.019) (0.027) (0.175)

No felleftout 0.189*** 0.232*** 0.016***

(0.022) (0.028) (0.028)

Fred of choice 0.089** 0.117** 0.008**

(0.033) (0.047) (0.004)

No fam resp.prevent 0.072*** 0.110*** 0.008***

(0.012) (0.017) (0.002)

No lack money 0.223*** 0.303*** 0.021***

(0.028) (0.032) (0.004)

Life has meaning 0.285*** 0.321*** 0.023***

(0.048) (0.051) (0.005)

Past good 0.255*** 0.338*** 0.024***

(0.044) (0.050) (0.005)

Vitality 0.167*** 0.216*** 0.015***

(0.029) (0.037) (0.003)

22

Opportunity 0.157*** 0.210*** 0.015***

(0.026) (0.034) (0.003)

Future good 0.367*** 0.472*** 0.033***

(0.030) (0.031) (0.006)

Constant 1.38*** - -

(0.37) - -

Observations 31185.000 31185.000 31185.000

R-squared 0.388 - -

Pseudo R-squared - 0.127 -

Log-Likelihood -54388.000 -50699.000 -

AIC 108799.700 101421.400 101421.400

BIC 108899.900 101521.500 101521.500

Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Reference Categories: Age class: 50-54; Marital Status: Single; Urban area: Rural; Country: France.

Table 6: Principal Component Analysis (PCA)

Component Eigenvalue Difference Proportion Cumulative

Comp1 4.10 2.78 0.37 0.37

Comp2 1.32 0.31 0.12 0.49

Comp3 1.01 0.22 0.09 0.59

Comp4 0.80 0.08 0.07 0.66

Comp5 0.72 0.04 0.07 0.72

Comp6 0.68 0.09 0.06 0.78

Comp7 0.58 0.06 0.05 0.84

Comp8 0.52 0.06 0.05 0.88

Comp9 0.46 0.02 0.04 0.93

Comp10 0.44 0.08 0.04 0.97

Comp11 0.37 - 0.03 1.00

Table 5: The Impact of Subjective Well-Being Sub-Components on Self-Declared Life Satisfaction (continued)


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Table 7: Correlations with the First Five Principal Components

Variable Comp1 Comp2 Comp3 Comp4 Comp5

Age no prevent 0.30 0.23 -0.36 0.19 -0.27

No out control 0.29 0.38 -0.39 -0.23 0.08

No feel left out 0.31 0.33 -0.25 -0.26 0.14

Fred. choice 0.27 -0.15 0.00 0.57 0.68

No fam. resp. 0.12 0.55 0.48 -0.05 0.36

No lack money 0.22 0.34 0.50 0.31 -0.44

Life has meaning 0.33 -0.27 0.11 -0.31 0.18

Past good 0.28 -0.23 0.36 -0.53 0.03

Vitality 0.36 -0.18 -0.16 0.11 -0.10

Opportunity 0.37 -0.24 0.07 0.13 -0.19

Future good 0.38 -0.20 0.08 0.09 -0.20

Table 8: The Determinants of Differences in Evaluating Vignettes

OLS OLOGIT

Variables Average-vignettes Vignette 1 Vignette 2

Female 0.017 0.026 0.046

(0.016) (0.047) (0.047)

Log income -0.028*** -0.076*** -0.051*

(0.009) (0.029) (0.028)

Education years -0.002 -0.015** 0.009

(0.002) (0.007) (0.007)

Household size -0.003 -0.011 0.001

(0.009) (0.027) (0.028)

Age class 55-59 -0.072*** -0.068 -0.243***

(0.025) (0.076) (0.077)

Age class 60-64 -0.044* -0.010 -0.183**

(0.026) (0.078) (0.080)

Age class 65-69 -0.121*** -0.232*** -0.312***

(0.029) (0.086) (0.088)

Age class 70-74 -0.155*** -0.241** -0.423***

(0.032) (0.095) (0.097)

Age class 75-79 -0.154*** -0.244** -0.441***

(0.036) (0.108) (0.110)

Age class above 79 -0.124*** -0.163 -0.389***

(0.036) (0.109) (0.110)

24

Leaving inheritance 0.016 0.047 0.048

(0.019) (0.056) (0.057)

Married -0.067* -0.235* -0.140

(0.040) (0.121) (0.123)

Widowed -0.089** -0.235* -0.223

(0.045) (0.135) (0.137)

Divorced -0.107** -0.397*** -0.111

(0.047) (0.143) (0.147)

Separated -0.075 -0.212 -0.168

(0.084) (0.258) (0.260)

Registered partner -0.041 -0.210 -0.010

(0.074) (0.225) (0.225)

N. of children 0.012 0.044* 0.011

(0.008) (0.023) (0.024)

N. of grandchildren -0.005 -0.000 -0.020*

(0.004) (0.011) (0.011)

Hrooms 0.003 0.016 -0.006

(0.006) (0.016) (0.017)

Big city -0.019 -0.077 -0.025

(0.026) (0.079) (0.078)

Suburbs -0.000 -0.117 0.120

(0.024) (0.073) (0.073)

Large town 0.006 0.018 0.030

(0.023) (0.068) (0.070)

Small town 0.041* 0.021 0.165**

(0.022) (0.065) (0.065)

Long-term illness -0.068*** -0.212*** -0.089

(0.019) (0.057) (0.057)

Limited activities 0.039** 0.111* 0.058

(0.019) (0.057) (0.058)

Numb illnesses -0.012** -0.014 -0.041**

(0.006) (0.019) (0.019)

Voluntary -0.010 -0.061 -0.018

(0.024) (0.071) (0.072)

Religion attendance 0.017 0.094 0.009

(0.025) (0.076) (0.076)

Political participation -0.018 -0.039 0.019

(0.037) (0.111) (0.114)

Table 8: The Determinants of Differences in Evaluating Vignettes (continued)


25

Help to family -0.029 -0.109* -0.018

(0.021) (0.061) (0.063)

Cared for sick -0.007 0.023 -0.013

(0.029) (0.085) (0.087)

Attended education 0.057* 0.065 0.166*

(0.030) (0.089) (0.091)

Sport social -0.010 -0.122** 0.051

(0.019) (0.058) (0.059)

Belgium 0.213*** 0.032 0.920***

(0.041) (0.124) (0.122)

Czech Rep. 0.474*** 1.064*** 1.101***

(0.045) (0.136) (0.134)

Spain 0.075 -0.220 0.512***

(0.049) (0.150) (0.144)

Germany 0.332*** 1.045*** 0.506***

(0.039) (0.119) (0.115)

Greece 0.137*** 0.384*** 0.137

(0.048) (0.147) (0.142)

Denmark 0.627*** 1.402*** 1.540***

(0.045) (0.135) (0.133)

Italy -0.040 -0.431*** 0.260**

(0.044) (0.135) (0.128)

Netherlands 0.135*** 0.528*** 0.221*

(0.045) (0.135) (0.134)

Poland 0.257*** 0.338** 0.794***

(0.046) (0.140) (0.138)

Sweden 0.147*** 0.071 0.556***

(0.051) (0.153) (0.149)

Constant 3.30*** - -

(0.05) - -

Observations 7154.000 7134.000 7131.000

R-squared 0.090 - -

Pseudo R-squared - 0.035 0.027

Log-Likelihood -6747.000 -8406.000 -8438.000

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Reference Categories: Age class:50-54; Marital Status:Single; Urban area:Rural; Country:France.

Table 8: The Determinants of Differences in Evaluating Vignettes (continued)

26





Imputation 2

Observations 30325 29411 30427 29411

R-squared 0.216 0.342 0.342 0.353

AIC 112843 76645.56 35823.81 111860.7

BIC 112942.8 76745.03 35923.69 111960.1

Imputation 3

Observations 30328 29414 30430 29414

R-squared 0.217 0.342 0.341 0.353

AIC 112826.2 76666.37 35836.53 111890.9

BIC 112926 76765.84 35936.41 111990.4

Imputation 4

Observations 30316 29404 30418 29404

R-squared 0.217 0.342 0.342 0.353

AIC 112809.2 76626.13 35807.17 111842.6

BIC 112909.1 76725.6 35907.04 111942.1

Imputation 5

Observations 30330 29416 30432 29416

R-squared 0.216 0.342 0.342 0.353

AIC 112856.5 76644.37 35819.32 111875

BIC 112956.3 76743.84 35919.2 111974.5

Table 10: Robustness Check of Table 3 with the Same Number of Observations (goodness of fit only)





Imputation 1

Observations 29354 29354 29354 29354

R-squared 0.218 0.341 0.342 0.352

Log-Likelihood -54462 -38221 -17149 -55796

AIC 108947.2 76466.86 34321.46 111616

BIC 109046.7 76566.31 34420.91 111715.4

Table 9: Robustness Check of Table 3 Estimates with the Four Alternative Imputations (goodness of fit only)


27

Table 11: Benchmark Model Estimated With Extended Predicted Life Satisfaction (11 sub-components interacted with country, gender, age and education dummies)

VARIABLES Happypred VARIABLES Happypred

Female -0.053* Number grandchildren 0.007**

(0.027) (0.003)

Log income 0.083*** Hrooms 0.025**

(0.015) (0.008)

Education years 0.025*** Big city 0.042

(0.006) (0.026)

Household size -0.027*** Suburbs 0.055**

(0.006) (0.019)

Age class 55-59 0.089*** Large town 0.081**

(0.017) (0.035)

Age class 60-64 0.126*** Small town 0.091**

(0.036) (0.041)

Age class 65-69 0.125*** Voluntary 0.102***

(0.038) (0.023)

Age class 70-74 0.097* Religion attendance 0.107***

(0.046) (0.032)

Age class 75-79 0.045 Political participation 0.063*

(0.044) (0.032)

Age class above 79 -0.055 Help to family 0.081***

(0.051) (0.016)

Leaving inheritance 0.250*** Austria 0.502***

(0.032) (0.029)

Married 0.201*** Belgium 0.280***

(0.044) (0.008)

Widowed 0.041 Czech Rep. -0.316***

(0.040) (0.033)

Divorced -0.028 Switzerland 0.881***

(0.055) (0.020)

Separated -0.005 Spain 0.241**

(0.072) (0.039)

Registered partner 0.220*** Germany 0.352***

(0.046) (0.007)

N. of children -0.012 Greece -0.172***

(0.008) (0.029)

Long-term illness -0.140*** Denmark 0.879***

(0.021) (0.037)

28

Limited activities -0.427*** Italy 0.811**

(0.044) (0.033)

Numb. illnesses -0.096*** Netherlands 0.583***

(0.010) (0.006)

Cared for sick -0.036 Poland -0.359***

(0.021) (0.042)

Attended education 0.029 Sweden 0.715***

(0.025) (0.041)

Sport social 0.121***

(0.027)

Constant 6.068***

(0.219)

Observations - 29414.000

R-squared - 0.404

AIC - 76365.050

BIC - 76464.520

Log-Likelihood - -38171.520

Robust standard errors in parentheses *** p<0.01,** p<0.05, * p<0.1 Reference Categories: Age class: 50-54; Marital Status: Single; Urban area: Rural; Country: France.

Table 12: The Determinants of Life Satisfaction Under Standard and Alternative Dependent Vari-ables (base model from table 3 estimated without health variables)





Female -0.019 -0.064* -0.031** -0.127**

(0.023) (0.030) (0.014) (0.055)

Log income 0.126*** 0.097*** 0.042*** 0.152***

(0.026) (0.016) (0.007) (0.026)

Education years 0.034*** 0.034*** 0.016*** 0.061***

(0.009) (0.008) (0.004) (0.013)

Household size -0.033* -0.021*** -0.014*** -0.027**

(0.015) (0.007) (0.004) (0.011)

Age class 55-59 0.004 0.039* 0.012 0.021

(0.024) (0.018) (0.009) (0.035)

Age class 60-64 -0.005 0.042 0.010 -0.001

(0.049) (0.037) (0.019) (0.073)

Table 11: Benchmark Model Estimated With Extended Predicted Life Satisfaction (11 sub-components interacted with country, gender, age and education dummies) (continued)


29

Age class 65-69 -0.005 0.001 -0.008 -0.107

(0.057) (0.045) (0.023) (0.089)

Age class 70-74 -0.029 -0.072 -0.053 -0.303**

(0.082) (0.060) (0.031) (0.115)

Age class 75-79 -0.067 -0.154** -0.097*** -0.518***

(0.078) (0.058) (0.031) (0.111)

Age class above 79 -0.111 -0.308*** -0.185*** -0.913***

(0.084) (0.060) (0.032) (0.110)


(0.051) (0.029) (0.013) (0.050)

Married 0.451*** 0.162*** 0.055*** 0.262***

(0.079) (0.035) (0.016) (0.059)

Widowed 0.020 -0.013 -0.007 -0.044

(0.064) (0.042) (0.020) (0.076)

Divorced -0.064 -0.099* -0.047* -0.125

(0.078) (0.054) (0.023) (0.092)

Separated -0.123 -0.038 -0.024 -0.028

(0.092) (0.068) (0.032) (0.114)

Registered partner 0.521*** 0.187*** 0.073** 0.325***

(0.089) (0.051) (0.025) (0.088)

N. of children 0.018* -0.008 -0.006 -0.005

(0.009) (0.007) (0.004) (0.013)

N. of grandchildren 0.003 0.000 -0.000 -0.003

(0.004) (0.002) (0.001) (0.005)

Hrooms 0.029** 0.033*** 0.013** 0.051***

(0.013) (0.010) (0.005) (0.017)

Big city 0.150** 0.077** 0.034* 0.152**

(0.050) (0.032) (0.017) (0.059)

Suburbs 0.053 0.078** 0.037** 0.147**

(0.069) (0.027) (0.013) (0.050)

Large town 0.142** 0.100** 0.050** 0.180**

(0.061) (0.041) (0.019) (0.073)

Small town 0.150* 0.126* 0.063** 0.226**

(0.070) (0.059) (0.029) (0.103)

Voluntary 0.131*** 0.123*** 0.068*** 0.251***

(0.031) (0.024) (0.010) (0.039)

Religion attendance 0.147** 0.102** 0.041* 0.166**

(0.055) (0.035) (0.019) (0.065)

Table 12: The Determinants of Life Satisfaction Under Standard and Alternative Dependent Vari-ables (base model from table 3 estimated without health variables) (continued)

30

Political participation 0.147*** 0.083** 0.039** 0.165**

(0.047) (0.038) (0.016) (0.065)

Help to family 0.108*** 0.089*** 0.039*** 0.200***

(0.029) (0.017) (0.009) (0.034)

Cared for sick -0.071* -0.054** -0.050*** -0.089*

(0.034) (0.023) (0.012) (0.043)

Attended education 0.038 0.038 0.006 0.079

(0.034) (0.026) (0.014) (0.048)

Sport social 0.157*** 0.156*** 0.078*** 0.320***

(0.028) (0.023) (0.011) (0.039)

Austria 0.486*** 0.284*** 0.112*** 0.369***

(0.036) (0.029) (0.013) (0.051)

Belgium 0.197*** 0.018* -0.022*** -0.089***

(0.011) (0.008) (0.004) (0.015)

Czech Rep. -0.499*** -0.562*** -0.290*** -1.035***

(0.039) (0.033) (0.015) (0.054)

Switzerland 0.937*** 0.487*** 0.208*** 0.812***

(0.029) (0.016) (0.007) (0.026)

Spain 0.267*** 0.004 -0.015 -0.063

(0.046) (0.036) (0.017) (0.065)

Germany 0.270*** 0.184*** 0.075*** 0.205***

(0.019) (0.011) (0.005) (0.018)

Greece -0.092* -0.293*** -0.205*** -0.605***

(0.042) (0.030) (0.014) (0.052)

Denmark 0.721*** 0.264*** 0.104*** 0.340***

(0.055) (0.032) (0.015) (0.056)

Italy 0.053 -0.215*** -0.164*** -0.524***

(0.037) (0.031) (0.015) (0.055)

Netherlands 0.526*** 0.559*** 0.237*** 0.824***

(0.013) (0.008) (0.005) (0.014)

Poland -0.486*** -0.211*** -0.121*** -0.400***

(0.046) (0.027) (0.013) (0.048)

Sweden 0.536*** 0.021 -0.007 -0.037

(0.068) (0.041) (0.018) (0.070)

Constant 4.910*** 5.746*** 2.325*** -2.782***

(0.284) (0.187) (0.083) (0.318)

Observations 30334.000 29422.000 30436.000 29422.000

R-squared 0.159 0.256 0.245 0.252



31

AIC 115002.200 80282.000 39996.020 116151.900

BIC 115102.000 80381.480 40095.900 116251.400

Log-Likelihood -57489.000 -40129.000 -19986.000 -58064.000

Robust standard errors in parentheses *** p<0.01,** p<0.05, * p<0.1 Reference Categories: Age class: 50-54; Marital Status: Single; Urban area: Rural; Country: France.

Table 13: The Determinants of Life Satisfaction Under Standard and Alternative Dependent Variables (base model from Table 3 estimated without health and social activity variables)





Female -0.016 -0.062* -0.031* -0.125**

(0.024) (0.030) (0.014) (0.057)

Log income 0.131*** 0.102*** 0.044*** 0.161***

(0.026) (0.017) (0.007) (0.027)

Education years 0.037*** 0.037*** 0.017*** 0.068***

(0.009) (0.008) (0.004) (0.013)

Household size -0.034** -0.024*** -0.015*** -0.032**

(0.014) (0.007) (0.004) (0.011)

Age class 55-59 0.005 0.036* 0.011 0.014

(0.025) (0.019) (0.010) (0.036)

Age class 60-64 0.003 0.045 0.012 0.003

(0.049) (0.037) (0.019) (0.073)

Age class 65-69 0.007 0.008 -0.004 -0.098

(0.056) (0.043) (0.023) (0.087)

Age class70-74 -0.020 -0.069 -0.050 -0.300**

(0.080) (0.059) (0.030) (0.112)

Age class 75-79 -0.073 -0.162** -0.100*** -0.540***

(0.075) (0.056) (0.030) (0.107)

Age class above 79 -0.143* -0.339*** -0.199*** -0.983***

(0.079) (0.057) (0.030) (0.101)


(0.052) (0.031) (0.015) (0.054)

Married 0.443*** 0.163*** 0.055*** 0.267***

(0.079) (0.033) (0.016) (0.059)

Widowed 0.022 -0.008 -0.006 -0.033

(0.069) (0.043) (0.021) (0.079)


32

Divorced -0.073 -0.094 -0.045* -0.113

(0.080) (0.055) (0.024) (0.094)

Separated -0.125 -0.030 -0.022 -0.016

(0.087) (0.069) (0.032) (0.114)

Registered partner 0.512*** 0.184*** 0.072** 0.322***

(0.093) (0.052) (0.026) (0.092)

N. of children 0.018* -0.007 -0.006 -0.004

(0.009) (0.007) (0.004) (0.013)

N. of grandchildren 0.003 0.000 -0.000 -0.002

(0.003) (0.002) (0.001) (0.005)

Hrooms 0.034** 0.038*** 0.015*** 0.062***

(0.013) (0.010) (0.005) (0.017)

Big city 0.145** 0.068** 0.030 0.136**

(0.053) (0.031) (0.017) (0.058)

Suburbs 0.046 0.068** 0.032** 0.132**

(0.071) (0.029) (0.014) (0.055)

Large town 0.138** 0.097** 0.049** 0.175**

(0.063) (0.042) (0.020) (0.074)

Small town 0.151* 0.126* 0.063* 0.225*

(0.073) (0.061) (0.030) (0.107)

Austria 0.479*** 0.281*** 0.109*** 0.363***

(0.034) (0.026) (0.012) (0.046)

Belgium 0.202*** 0.024*** -0.021*** -0.077***

(0.011) (0.007) (0.003) (0.012)

Czech Rep. -0.553*** -0.608*** -0.312*** -1.130***

(0.042) (0.034) (0.016) (0.058)

Switzerland 0.965*** 0.515*** 0.219*** 0.866***

(0.031) (0.017) (0.008) (0.028)

Spain 0.223*** -0.031 -0.032* -0.140**

(0.044) (0.032) (0.015) (0.059)

Germany 0.260*** 0.180*** 0.072*** 0.195***

(0.017) (0.010) (0.005) (0.017)

Greece -0.105** -0.310*** -0.214*** -0.647***

(0.041) (0.027) (0.012) (0.045)

Denmark 0.746*** 0.286*** 0.114*** 0.385***

(0.057) (0.034) (0.015) (0.059)

Italy 0.010 -0.251*** -0.181*** -0.599***

(0.035) (0.028) (0.013) (0.050)

Table 13: The Determinants of Life Satisfaction Under Standard and Alternative Dependent Variables (base model from Table 3 estimated without health and social activity variables) (continued)


33

Netherlands 0.563*** 0.593*** 0.252*** 0.894***

(0.011) (0.008) (0.004) (0.013)

Poland -0.545*** -0.256*** -0.142*** -0.494***

(0.044) (0.021) (0.010) (0.038)

Sweden 0.569*** 0.051 0.005 0.025

(0.064) (0.040) (0.018) (0.068)

Constant 4.898*** 5.725*** 2.317*** -2.824***

(0.288) (0.197) (0.086) (0.339)

Observations 30519.000 29593.000 30624.000 29593.000

R-squared 0.154 0.247 0.236 0.242

AIC 116016.800 81147.490 40658.840 117308.600

BIC 116116.800 81247.030 40758.790 117408.100

Log-Likelihood -57996.000 -40561.740 -20317.000 -58642.000

Robust standard errors in parentheses *** p<0.01,** p<0.05, * p<0.1Reference Categories: Age class: 50-54; Marital Status: Single; Urban area: Rural; Country: France.

Table 13: The Determinants of Life Satisfaction Under Standard and Alternative Dependent Variables (base model from Table 3 estimated without health and social activity variables) (continued)

34

1. Frey and Stutzer (2002a, 2002b).

2. The main contributions in this field are those valuing air pollution (Welsch, 2002), terrorist activity (Frey et al., 2009), noise nuisance (van Praag & Baarsma, 2005) and flood disasters (Luechinger & Raschky, 2009).

3. King and Wand (2007); Corrado and Weeks (2010).

4. Vignette equivalence requires that the scenarios in the vignettes are perceived with no systematic differences across respondents. Response consistency requires that individuals use the response category in the self-assess-ment question in the same way as when they evaluate hypothetical scenarios in the vignettes.

5. Bago d’Uva et al. (2011); Ferrer-i-Carbonell et al. (2010); Corrado and Weeks (2010).

6. In order to harmonize the response scale of the 11 sub-components with the response scale of the synthetic question on life satisfaction we have re-ordered the response scale of the five sub-components denoting positive dimensions of well-being (questions 4 and 7-11) as follows: never=1, rarely=2, sometimes=3, often=4. For the five sub-components denoting negative dimensions of well-being (questions 1-3 and 5-6) the response scale are left unchanged: 1=often, 2=sometimes, 3=rarely, 4=never.

7. Inglehart and Klingemann (2000); Eurobarometer (2002); Corrado and Weeks (2010); Kapteyn, Smith, & Soest (2007).

8. Corrado and Weeks (2010) examine the use of vignettes to correct for the different use of response scales when rating life satisfaction. They show that these additional questions can, under certain conditions, be used to correct for the resultant biases in model parameters. The bias is found especially for top ranked countries such as Denmark thereby confirming that country rankings reflect not just the true variation in life satisfaction but a different use of the response scales and more optimistic evaluations of life of certain countries and cultures (see also Kapteyn, Smith, and Soest, 2007).

9. See Golderberg and Williams (1988).

10. For simplicity and without lack of generality we assume that the weights are common to each individual. The idea of happiness fundamentals that are common to all individuals in different countries is, in some way, supported by the empirical literature showing that determinants of subjective wellbeing are quite similar across different countries and time periods (Becchetti et al., 2010).

11. In the context of attitudinal surveys where observed responses are often discrete, the disjunction between what is observed and the underlying latent measurement error in the dependent variable is generally understood as

arising from an error in either recording or reporting of a response. Corrado and Weeks (2010) analyse different solution methods to correct for response scale heteroge-neity when responses are discrete.

12. If measurement error affects one or more explanatory variables, this will generate biased and inconsistent parameter estimates, with a general tendency towards attenuation. Kreider (1999) discusses the problem of measurement error for self-reported health and in particular work disability in the context of models of labour force participation. However, the focus here is the impact of likely overreporting of disability on parameter estimates associated with one or more explanatory variables whereas our focus is on measurement error affecting the dependent variable.

13. Life satisfaction is ordinal, so that its panel estimation would require something like a ordered probit or conditional fixed effect logit (as in Clark, 2003). However, as Ferrer–i–Carbonell and Frijters (2004) argue, Cardinal estimation seems to perform just as well as ordinal estimation when life satisfaction is measured on the 0-10 scale (Ferrer–i–Carbonell & Frijters, 2004).

14. See Bound, J., Brown, C., & Mathiowetz, N. (2001).

15. All the above-mentioned methods involve introducing external information. A number of authors have suggested instrumental variable estimators that use third or higher moments of the variables as instruments for or (Cragg, 1997; Dagenais & Dagenais, 1997; Lewbel, 1997). Alternatively, Wald (1940) suggested an estimator which involves grouping the data. However, unless some external information can be used to form groups (i.e. an instrument) is available, the resulting estimator will typically be no less biased than OLS (Pakes, 1982).

16. In a non-linear regression model, such as a probit model, the effects of measurement error are more severe. If the dependent variable is binary, measurement error takes the form of misclassification errors; some observations where the variable is truly a 1 will be misclassified as a 0 and vice versa. In this case the measurement error is negatively correlated with the true variable. This can lead to coefficient estimates that are biased and inconsistent.

17. The Akaike Information Criterion (AIC) is defined as and the Bayesian Incformation Criterion (BIC) as where denotes the number of observations, is the number of parameters and denotes the Residual Sum of Squares In presence of measurement error the Residual Sum of Squares will be higher, hence both the and will be higher indicating a poorer fit of the model. The adjusted defined as will be, instead, lower.

18. Last Release 2.5.0: May 24, 2011 available at http://cdata8.uvt.nl/sharedatadissemination/releases/show/ w2_250/All+CAPI+modules/stata.

35

19. See Ferrer-i-Carbonell, A., & Frijters, P. (2004).

20. See also Ferrer-i-Carbonell (2004, 2008) on this point.

21. The dataset used is “ sharew2_rel2-5-0_imputations”.

22. Van Buuren, S., Brand, J.P.L., Groothuis-Oudshoorn, C.G.M., & Rubin, D.B. (2006).

23. A key aspect of the FCS method is that it operates under the missing at random (MAR) assumption where the missing-ness of each variable depends only on other variables in the system and not on the values of the variable itself. In the iteration process, the initial conditions of the first iteration are derived by imputing the first variable in the system based only on the variables that are never missing (age, gender and geographic location), then the variables in the second iteration are calculated based on the first and the non-missing variables, in order to achieve a complete set of values for these initial conditions. In this calculation the fully imputed demographic variables are used as predictors for the economic variables; in the imputation of a specific wave, large part of information that comes from other waves is taken into account. The imputation in SHARE also allows an initial burn-in period in order to decrease the dependence of the chain on the initial values. Five burn-in iterations are used by evaluating the Gelman-Ru-bin criterion from the seventh iteration on. For more details see Christelis (2011).

24. Ireland is excluded from this procedure.

25. The imputed datasets are available from SHARE at http://cdata8.uvt.nl/sharedatadissemination/releases/show/.

26. w2_250/Generated+Variables/Imputations/stata.

27. As it is well known the VIF (variance inflation factor) formula is where is the -squared obtained by regress-ing each independent variable on all other independent variables (Marquardt, 1970). If is low (tends to zero) the VIF test is low (equal to one).

28. Since our sample is made by people aged above 50, this apparently surprising result may capture the ascending part of the U-shaped relationship between age and happiness (see among others Clark et al., 1996 and Frijters and Beatton, 2008).

29. See Kaiser, H., & Rice J. (1974).

30. The first vignette is “John is 63 years old. His wife died 2 years ago and he still spends a lot of time thinking of her. He has 4 children and 14 grandchildren who visit him regularly. John can make ends meet but cannot make for extra such as expensive gifts for his grandchildren. He has had to stop working recently due to heart problems. He gets tired easily. Otherwise he has not serious health conditions.” The second vignette is “ Carry is 72 years old and a widow. Her total after tax income is about 1,100 per month. She owns the house she lives in and has a large circle of friends. She plays bridge twice a week and goes on vacation regularly with some friends. Lately she has been suffering from arthritis, which makes working in the house and garden painful.”

31. See Inglehart and Klingemann (2000); Eurobarometer (2002); Corrado and Weeks (2010) Kapteyn, Smith, & Soest (2007).

32. See Christelis, D. (2011).

33. See Goldberg, D., & Williams, P. (1988).


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